Just had a few thoughts about the workprint for you.

I think it's important that you not remove the scene where Gandalf tells Frodo about Gollum. The thing about pity is a driving force for how Frodo treats Gollum.

I know you don't want to, but I second the idea of going right from Balin's tomb to the bridge without the fight scene. It's a good way to knock off a few minutes that don't further the plot, especially since there's no mithril anyway.

The prologue has too much backstory to be safely removed, but perhaps you could begin the film with Gandalf's arrival at the Shire, and put bits and pieces of the prologue where they'd go. (The Last Alliance battle when Gandalf reads up on Isildur, etc.)

Unrelated to any ulterior "purist" motives, cutting the elves from Helm's Deep offers another way to shave off some precious minutes. Their presence in the film was a necessity from the semi-cancelled involvement of Arwen and Elrond in the battle. You could cut the battle for Helm's Deep altogether and really save some time. Rohan could go from Theoden regaining his right mind into the scenes after the battle is over, leaving the Ents to take care of Saruman.